Fuzzy set-based uncertainty analysis of HVAC&R systems: a simulation study

Abstract

The accuracy of model predictions plays an important role in model-based applications. However, mathematical models exhibit more or less uncertainties. In this study, a full-scale dynamic model of a two-zone variable air volume heating, ventilation, air-conditioning and refrigeration (VAV-HVAC&R) system is considered. A fuzzy set-based uncertainty analysis method is employed to study the effects of uncertain parameters on HVAC&R system modelling and describe the associated inaccuracies in HVAC&R system model predictions. In this study, uncertain parameters, i.e. zone cooling loads, heat transfer coefficient, chilled water and condenser water mass flow rate and water temperature at condenser inlet are considered and treated as fuzzy parameters. The extended transformation approach is used to evaluate the uncertainties in the model outputs including time history of the zone temperature, discharge air temperature, temperature of chilled water and condenser water. The upper and lower bounds of these outputs are determined for each a-cut level, and the probability distributions of the outputs are presented. Practical applications: Compared to monitoring of real systems, model-based simulation provides an easier, faster and cheaper substitute to gather operating information and evaluate operating performance of HVAC&R systems. However, simulation results obtained from traditional methods by which model equations are solved with predetermined values cannot accurately represent the possible responses of the system. Thus investigating the probability distributions of the simulation results under parameter uncertainties is very important to ensure the accuracy of the model predictions. The fuzzy set-based uncertainty analysis method presented here helps in identifying the upper and lower bounds of model outputs by quantifying the range within which the responses fall under parameter uncertainties. Also, the contributions of individual uncertain parameters to the uncertainties of model outputs help in identifying the impact parameters.